The invention relates in general to a statistical process control (SPC) method applicable in situations where the post-stage process is related to the pre-stage process, and more particularly to a SPC method capable of separating the influence of the variation of the pre-stage process from that of the post-stage process.
The method of statistical process control (SPC) has been applied for improving the product quality in many manufacturing processes after Dr. W. A. Shewhart drew the first SPC chart in 1924 and published the article “Economic Control of Quality of Manufactured Products” in 1931. The SPC method involves using statistical techniques to measure and analyze the variation in the processes and aims to keep the processes under control. No matter how good or bad the design, SPC can ensure that the product is being manufactured as designed and intended. Thus, SPC will not improve the reliability of a poorly designed product, but it can be used to maintain the consistency of how the product is made, and therefore, of the manufactured product itself and its reliability as designed.
The measured data in the SPC chart usually varies within a certain range by some reasons, which are classified as either permissible factor (within the control) or excessive factor (out of the control). While the products are processed only with some permissible factors, the manufacturing will be stable and the variation of the product quality character will be within a predictable and controllable range. If the products are processed with some permissible factors and some excessive factors, the manufacturing will be unstable and the variation of the product character will be out of a statistical control range. Therefore, the inline SPC system can detect the occurrence of excessive factor and improve the product manufacturing quality thereby.
Referring to FIG. 1, it shows a SPC scatter plot for monitoring semiconductor manufacturing according to a traditional method, wherein the vertical axis represents the critical-dimension measurement after etching and the horizontal axis represents the time. The average of the critical-dimension measurements is represented by solid line of y=u, and the upper and lower control limits are represented by the dashed lines of y=u+3σ and y=u−3σ, respectively, where σ is the standard deviation of the measurements.
There are 1030 times of sampling measurements in FIG. 1, which are measured and collected under a stable photolithography process followed by a stable etching process. However, the SPC method delivers a warning message because of 6 measurements found to be out of the control limits, wherein the 6 measurements exceed by 3 measurements under the same sampling number, being expected to be out of the control limits with 99.73% possibility by three sigma (3σ) standard deviation. This is because a dependent relation exists between the photolithography process and the etching process, and the variation of the critical dimension measurements for the etching process is affected by that in the photolithography process.
FIG. 2 shows the dependent relation between the photolithography process and the etching process, wherein the vertical axis represents the etching critical dimension measurements and the horizontal axis represents the photolithography critical dimension measurements. Under such existing distributional relation between the post-stage and the pre-stage, the traditional SPC system is no longer able to provide the correct information and accordingly loses its monitoring function.
Against the traditional method, the SPC method with non-constant mean is disclosed in U.S. Pat. No. 5,987,398, wherein the average of the film thickness, y=u, is modified to a decreasing value. The method is especially applicable in the sputtering process, wherein the metal target decreases in the continuing process and the thickness of the deposited metal film becomes thinner during a certain period of time. However, the SPC method with non-constant mean cannot solve the problem that the variation of the pre-stage process affects that of the post-stage process.